Proving Newton’s Second Law of Motion
Aim: Prove that a (acceleration) is proportional to the net force and inversely proportional to the mass.
Background Theory: Sir Isaac Newton presented his three laws of motion in the Principia Mathematica Philosophiae Naturalis in 1687. The second law, ΣF = ma, states that changes in force will cause an object to accelearate and with this equation, one can figure out how much. It can be rewritten into a = ΣF / m, and thus, it can be seen that acceleration is proportional to net force and inversely proportional to mass. In this experiment, the acceleration of a cart which moves due to the force of the hanging weight pulling it down will be measured. The mass of the cart and hanging weight will be changed. If the changes and …show more content…
So
ΣFY = Fg - FN = 0
Since the hanging weight and cart are connected through a string connected to the pulley, the tension force of the hanging weight equals the x-force of the cart. Thus, we can write tension:
FX-cart = mcarta = T
And it is also known that the force that causes the hanging weight to accelerate is equal to the sum of the forces acting upon it.
ΣFY-hanging = mhanginga = mhangingg - T
With that, we can replace the T in our second equation for the T in our first equation and do some simple algebra to find the formula for the theoretical acceleration. mhanginga = mhangingg - mcarta mhangingg = mhanginga + mcarta a = mhangingg / (mhanging + mcart)
Results:
Table 1 - Changing cart mass
Table 2 - Changing hanging weight
Aim: Prove that a (acceleration) is proportional to the net force and inversely proportional to the mass.
Background Theory: Sir Isaac Newton presented his three laws of motion in the Principia Mathematica Philosophiae Naturalis in 1687. The second law, ΣF = ma, states that changes in force will cause an object to accelearate and with this equation, one can figure out how much. It can be rewritten into a = ΣF / m, and thus, it can be seen that acceleration is proportional to net force and inversely proportional to mass. In this experiment, the acceleration of a cart which moves due to the force of the hanging weight pulling it down will be measured. The mass of the cart and hanging weight will be changed. If the changes and …show more content…
So
ΣFY = Fg - FN = 0
Since the hanging weight and cart are connected through a string connected to the pulley, the tension force of the hanging weight equals the x-force of the cart. Thus, we can write tension:
FX-cart = mcarta = T
And it is also known that the force that causes the hanging weight to accelerate is equal to the sum of the forces acting upon it.
ΣFY-hanging = mhanginga = mhangingg - T
With that, we can replace the T in our second equation for the T in our first equation and do some simple algebra to find the formula for the theoretical acceleration. mhanginga = mhangingg - mcarta mhangingg = mhanginga + mcarta a = mhangingg / (mhanging + mcart)
Results:
Table 1 - Changing cart mass
Table 2 - Changing hanging weight